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 A069811 a(n) = Sum_{k=1..n} omega(k)^2. 3
 0, 1, 2, 3, 4, 8, 9, 10, 11, 15, 16, 20, 21, 25, 29, 30, 31, 35, 36, 40, 44, 48, 49, 53, 54, 58, 59, 63, 64, 73, 74, 75, 79, 83, 87, 91, 92, 96, 100, 104, 105, 114, 115, 119, 123, 127, 128, 132, 133, 137, 141, 145, 146, 150, 154, 158, 162, 166, 167, 176, 177, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Fifth edition, Oxford University Press, Chap. XXII, p. 357. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 Paul Turán, On a theorem of Hardy and Ramanujan, Journal of the London Mathematical Society, Vol. s1-9, No. 4 (1934), pp. 274-276. FORMULA a(n) = Sum_{k=1..n} A001221(k)^2. a(n) = n*log(log(n))^2 + O(n*log(log(n))) (Turán, 1934). a(n) = Sum_{k>=1} k^2 * A346617(n,k). - Alois P. Heinz, Aug 19 2021 MATHEMATICA Accumulate@((PrimeNu@Range@62)^2) (* Ivan Neretin, Mar 16 2017 *) PROG (PARI) a(n) = sum(k=1, n, omega(k)^2); \\ Michel Marcus, Mar 16 2017 CROSSREFS Equals (A074787(n)-1)/4 for n <= 29. Cf. A001221, A346617. Sequence in context: A061887 A005455 A047338 * A004826 A326783 A326785 Adjacent sequences: A069808 A069809 A069810 * A069812 A069813 A069814 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Apr 30 2002 STATUS approved

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Last modified February 29 04:20 EST 2024. Contains 370401 sequences. (Running on oeis4.)